The diameter of a wire is measured as 0.25 cm using a screw gauge of least count 0.005 cm. The percentage error is

Options

A. `1%`
B. `2.5%`
C. `5%`
D. `2%`

Answer

To find the percentage error in the measurement of the diameter of a wire, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Measured diameter of the wire (D) = 0.25 cm
- Least count of the screw gauge (LC) = 0.005 cm

2. **Calculate the percentage error:**
The formula for percentage error is given by:
\[ \text{Percentage Error} = \left( \frac{\text{Least Count}}{\text{Measured Value}} \right) \times 100 \]

3. **Substituting the values into the formula:**
\[ \text{Percentage Error} = \left( \frac{0.005 \text{ cm}}{0.25 \text{ cm}} \right) \times 100 \]

4. **Perform the division:**
\[ \frac{0.005}{0.25} = 0.02 \]

5. **Multiply by 100 to find the percentage:**
\[ 0.02 \times 100 = 2\% \]

6. **Final Result:**
The percentage error in the measurement of the diameter of the wire is **2%**.